Multi-channel sound signal generating and reproducing circuits

ABSTRACT

An arrangement of a multi-channel sound circuit wherein a plurality of original electric signals produced from a plurality of sources of sound signals as arranged on a plane are converted into a plurality of transmission channel signals by means of a matrix circuit which shifts the phases of the electric signals by amounts proportional to the azimuths of the sound signals, respectively, and which adds the electric signals, and wherein the original sound signals are reproduced from the transmission channel signals by means of a circuit which has the same arrangement as the matrix circuit, said matrix circuit involving a plurality of factor matrices, and having an element 1 in each matrix formed of a first phase shifter circuit and an element neither 1 nor 0 formed of a second phase shifter circuit, the phase difference between the first and second phase shifter circuits being made a predetermined value, whereby the matrix circuit is arranged simply and economically.

United States Patent [1 1 Nakano Dec. 9, 1975 1 MULTI-CHANNEL SOUND SIGNAL GENERATING AND REPRODUCING CIRCUITS [75] Inventor: Yasuaki Nakano, Hino, Japan [73] Assignee: Hitachi, Ltd., Japan [22] Filed: Feb. 26, 1973 [21] Appl. No.: 335,741

[44] Published under the Trial Voluntary Protest Program on January 28, 1975 as document no.

OTHER PUBLICATIONS Analysing Phase Amplitude Matrices, by Scheiber, AES Preprint, Oct. 1971.

4TRANSM|SS|ON CHANNEL RECIEVER Multichannel Stereo Matrix Systems: An Overview by Eargle Journal ABS, July/August 1971. Discrete-Matrix Multichannel Stereo, by Cooper & Shiga, Journal ABS, June 1972, presented 10/7/71.

Primary ExaminerK. Claffy Assistant ExaminerThomas DAmico Attorney, Agent, 0r FirmCraig & Antonelli [57] ABSTRACT An arrangement of a multi-channel sound circuit wherein a plurality of original electric signals produced from a plurality of sources of sound signals as arranged on a plane are converted into a plurality of transmission channel signals by means of a matrix circuit which shifts the phases of the electric signals by amounts proportional to the azimuths of the sound signals, respectively, and which adds the electric signals, and wherein the original sound signals are reproduced from the transmission channel signals by means of a circuit whichhasthe same arrangement as the matrix circuit, said matrix circuit involving a plurality of factor matrices, and having an element 1 in each matrix formed of a first phase shifter circuit and an element neither 1 nor 0 formed of a second phase shifter circuit, the phase difference between the first and second phase shifter circuits being made a predetermined value, whereby the matrix circuit is arranged simply and economically.

8 Claims, 6 Drawing Figures US. Patent Dec. 9, 1975 Sheet 2 of3 3,925,615

4TRANSM|SSION CHANNEL 20a 20b 20c 20d US. Patent Dec. 9,1975 Sheet 3 of3 3,925,615

A I v O2w30mwE MULTI-CHANNEL SOUND SIGNAL GENERATINGv AND REPRODUCING CIRCUITS BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to improvements in multi-channel sound signal generating and reproducing circuits. More particularly, it relates to improvements in multi-channel sound signal generating and reproducing circuits in a system in which a plurality of arrayed original sound signals are combined to transmit them by a plurality of transmission channels or to record them in a plurality of recording channels, and the original sound signals are reproduced from the transmitted or recorded signals.

2. Description of the Prior Art I-Ieretofore, there have been published a number of multi-channel sound signal generating and reproducing systems such as a 4-channel stereophonic record player system. Any of the systems, however, have not only merits but also demerits, and are not definitive.

Recently, Duane H. Cooper and Takeo Shiga published a system at the 1971 meeting of the American Audio Engineering Association. The system (hereinafter termed the universal matrix system") is excellent in its compatibility with monophonic and biphonic systems, and is a hopeful method.

The universal matrix system will now be explained. Although, in order to simplify the explanation, the case of 4 sound sources, 4 transmission channels and 4 reproduction channels will be referred to, it is apparent that amplification can be readily made to the other cases.

Theequation of a matrix is a square matrix of the same number of order as the number of sound sources. The elements of the matrix are represented by r (where 7- denotes the minimum angle of the azimuths of the sound sources, and i andj rows and columns, respectively). The four signal sources (forexample, electric signals obtained from microphones) arranged in such manner thattheir azimuths on a plane are spaced by every 90, are represented by S S S and S In the universal matrix system, the signals of the four signal sources are compounded according to the following equation, to make 4-channel signals, and then, they are sent to recording channels of a recording medium such as a phonograph record or to transmission lines for broadcasting or the like (hereinbelow, generically termed the transmission channels).

T 1 z t t (1) 1 z 2 6 T2 1 'L C r 5 T5 1 '0 L I9 In the above eq. 1, 'r is a symbol representative of a phase shift of 90. 1' represents a phase shift of 180, 1 one of 270, Eq. (1) is calculated in conformity with the usual rules of arithmetics of vector and matrix.

In. the reproduction system, the original signals are restored from the four transmitted or recorded signals T T T and T in accordance with:

P 1 1 1 1 T P 1 'r' 'r' 'r" T P 1 T T T The coefficient 1 on the right of the above eq. 2 is not .important, and may be omitted.

In Eq. 2, 'r signifies a phase shift ofnamely, one of 270. F 1*, 7 signify phase shifts of- 180, 270, 360, respectively.

The procedure of Eq. 1 is considered to be coding, and that of Eq. 2 decoding (herein, however, pulse coding as in PCM is not meant). If the coding, transmission and decoding are perfectly performed, there holds:

and the original sound sources can be reproduced. This produces the same result as that of the so-called discrete system in which individual sound source signals are reproduced through separate transmission lines or recording channels of a recording medium.

When only one transmission line or T can be utilized in the universal matrix system, the system is compatible with the monophonic system. This is apparent by substituting the following into Eq. 2:

T] T2 T3 0 Similarly, in case of two transmission lines, only '1 and T are utilizable. This case falls under the so-called 4 2 4 system consisting of 4 signal sources, 2 transmission lines and 4 reproduction channels. With the universal matrix system, it becomes the matrix quasi-4- channel system.

In this manner, the universal matrix system provides the reproduced signals of 4 channels with the identical restoration matrix in any of the cases where the numbers of the transmission lines are l, 2, 3 and 4. The azimuth angles of the reproduced sounds are sharper as the number of the transmission lines is larger. For example, in the case of 8 channels, the azimuth is as sharp as 45, and in case of 16 channels, it is as sharp as 225. This feature is advantageous in building up a reproduction system.

The universal matrix system, however, is more complicated in the arrangement of coding matrix and decoding matrix circuits than the discrete system. Since it is not efficient to realize the circuit of the matrix of Eq. 1 or Eq. 2 as it is, Eqs. 1 and 2 can be respectively rewritten into the following equations 1' and 2 by making use of such relations as r =1, 1' =1, 1' l and F l. i

1 1 I: ""1 Z (1' i T5 1 'L -1 A -1 P 1 -z z 1 Even with the reductions, however, the circuit arrangements for the equations of the matrices are complicated. For example, the circuit of Eq. 2' is as shown in FIG. 2.

In particular, the arrangement of phase shifter circuits is complicated in such circuits. It is therefore required to lessen the number of the phase shifter circuits as far as possible.

While, in the foregoing, the case of 4 channels has been exemplified, the matrix circuits become largesized in proportion to the square of the number of channels, respectively, and hence, an increase in the number of channels is unsuitable for practical use.

SUMMARY OF THE INVENTION The principal object of the present invention is to simplify the arrangement of multi-channel sound signal generating and reproducing circuits according to the universal matrix system.

Another object of the present invention is to bring into simple arrangements, matrix circuits of the aforesaid muli-channel sound signal generating and reproducing circuits of the universal matrix system.

Still another object of the present invention is to reduce the number of phase shifters constituting the matrix circuits.

In order to accomplish the objects, the present invention is constructed such that a matrix providing a multichannel sound signal generating or reproducing circuit is factorized on the basis ofthe periodicity of the matrix in the universal matrix system, that the factorized matrix is put into circuit components or contituents, and that they are connected in cascade.

The above-mentioned and other objects and features of the present invention will be made more apparent from the following drawing and the explanation thereof.

BRIEF DESCRIPTION OF THE DRAWING FIG. 1 is a block diagram showing the construction of the universal matrix system;

FIG. 2 is a connection diagram of a prior-art matrix circuit of a 4-channel sound signal reproducing circuit in the universal matrix system;

FIGS. 3 and 4 are connection diagrams each showing an embodiment of a matrix circuit for use in a 4-channel sound signal generating circuit according to the present invention;

DESCRIPTION OF THE PREFERRED EMBODIMENTS FIG. 1 is a block diagram showing the construction of the universal matrix system to which the present invention is applied, and particularly illustrates 4-channel sound signal generating and reproducing circuits. As shown in the figure, four signal sources, such as microphones, 2a 2d are provided for a sound source 1 in such manner that the azimuths are spaced by every Output signals sent out from the signal sources are represented by S S S and S respectively. The respective signal outputs are transformed into 4-channel signals. T T,, T T by means of a 4-channel sound signal generating circuit or coding circuit 3. The transformed signals are sent out to recording channels of a recording medium such as a sound recording disc, or transmission lines for broadcasting or the like (hereinafter generically called the transmission channels") 4.

Outputs from the transmission channels 4 are reproduced into signals P P P and P by means of a 4- channel sound signal reproducing circuit or decoding circuit 5. The reproduced signals are converted into sound signals by means of four electroacoustic transducers, such as speakers, 7a 7d which are respectively arranged around a listener 6. In this case, the number of the transmission channels 4 is not necessarily required to be four, but a sound effect as in the case of four channels is achieved even with two or three chan nels be appropriately constructing the coding circuit 3 and the decoding circuit 5. The relations of Eqs. l. 2 and 3 as previously stated. apply to the signals S S T T and P P FIG. 2 shows a prior-art circuit of the 4-channel sound signal reproducing circuit 5 as constructed on the basis of Eq. 2. If the signals T T,. T and T are changed into: S 5,. S and S in the circuit. respectively. the 4-channel sound signal generating circuit 3 will be constituted.

Referring to the figure. the signals T, T derived from the transmission channel 4 are applied to input terminals 80. 8h. 80 and 8d. Among the signals. T and T are fed to adders 10a and via phase shifter circuits A including 9a2. 9u4 and 94'2. 904 and to adders I0!) and I011 via phase shifter circuits B including 9h2.

v (with marks O) and the phase shifter circuits B (with marks O) have a phase difference of 90 therebe'tween. Preferably, the amplitude-versusfrequency characteristics of the respective phase shifters are as flat as possible. The adders a to 10d effect the matrix operation of Eq. (2' and send out output signals to output terminals 4a to 4d, respectively.

In the circuit in FIG. 2, the 16 phase shifter circuits are used in total as the phase shifter circuits A and B.

The phase shifters, however, are complicated in construction or circuit arrangement. Unless, in particular, the accuracy of phase shift is made as high as possible, the operation of the aforesaid matrix cannot be conducted precisely, and an error in the restoring circuit 5 and one in the coding circuit 3 will be superposed.

Both FIG. 3 and FIG. 4 show embodiments of the matrix circuits according to the present invention as constitute the 4-channel sound signal reproducing circuit in the universal matrix system. Of course, if the transmission channel signals T T T and T in FIGS. 3 and 4 are replaced with the sound source signals S 8,, S2 and S the 4-channel sound signal generating circuit 3 will be provided on the ground of Eq. 2 Eq. 2 and the relations of 1' representative of the phase shift of 90 and F representative of that of 90. Accordingly, although the 4-channel sound signal reproducing circuit will be described hereunder, the 4-channel sound signal generating circuit is of quite the same construction.

When the matrix of Eq. 2 is factorized, it is expressed as in the following equation 4:

Ol- Oi- HOl-O Or, the symmetry is made clearer in such way that the sequence of vectors on the right of Eq. 4 is changed as in the following equation 4':

P 1 0 1 O l l O 0 To P O 1 O r 1 -1 O 0 T P 1 O 1 O 0 O 1 1 T1 P 0-] Or 0 011 T A circuit arranged on the basis of Eq. 4 is as shown in FIG. 3.

Referring to the figure, an input unit 12 is a phonograph pickup in case of the reproduction ofa disc, and a receiving set in case of the reception of broadcasting. Herein, it generally denotes a receiver for transmission signals. The input device 12 receives the 4-channel transmission signals, and delivers the signals T T T and T of Eq. 2 from output terminals 13a 13d. Since some vector components are replaced in Eq. 2, connections are crossed in the illustration of FIG. 3.

The signals T T transmitted from the input device 12 are applied to adders 14a 14d in such manner that two of them are combined as shown. Outputs of the adders 14a 14d are equivalent to multiplications of the vectors by the second one of the factorized matrices on the right of Eq. 4'. Subsequently, the outputs of the adders 14a are respectively applied to phase shifter circuits A at 15a 150, while the output of the adder 14d is applied to a phase shifter circuit B at 15d. As shown in the figure, outputs of the phase shifter circuits are applied to adders 16a 16d with two of them combined. In this case, the adders 16a 16d function to multiply vectors by the first matrix on the right of Eq. 4, the vectors being obtained by the multiplications between the second matrix and the vectors previously referred to.

In the above explanation, all the adders 14b, 14d and 16c, 16d are supposed to have subtraction terminals. It is also possible, however, that all the adders comprise only addition terminals and that phase inverter circuits are used in place of the subtraction terminals. Further, if a circuit simultaneously providing a positive phase output and a negative phase output is employed, the

l O l 0 T 0 l O 1 T 1 O l 0 T 0 l O 1 T phase inverter circuit will not be necessary either. At the next step, outputs of the adders 16a 16d are respectively connected to output terminals 17a 17d, and the reproduced outputs of 4 channels are obtained.

As apparent from the circuit in FIG. 3, in accordance with the embodiment, the construction becomes simple in comparsion with the circuit in FIG. 2. Since the four phase shifter circuits suffice, the matrix circuit can be manufactured inexpensively.

It is as previously stated that, when only two inputs are utilizable in the input unit 12 in the circuit of FIG. 3, the reproduction of the quasi-4-channel system is available by the use of only T and T of the input signals T T In this case, the terminals of T and T may be grounded and brought into no signal.

Another embodiment according to the present invention will now be described with reference to FIG. 4. The embodiment simplifies the construction of FIG. 3 by employing multi-input terminal adders. The input unit 12, output terminals 13a 13d, adder 14d and phase shifter circuit 15d are the same as in FIG. 3. Output terminals a 20d correspond to those 17a 17d in FIG. 3. Phase shifter circuits A at 18a 18d are provided in order to hold phasic relations as in the case of FIG. 3. Adders 19a 19d are the mult-input terminal adders. The adder 190 is constructed by putting the adders 14a, 14c and 16a in FIG. 3 together, while the adder 19c by bringing the adders 14a, 14c and 16c. The adders 19b 19d have subtraction terminals in the illustrated embodiment. As previously stated, however, it is also allowed to employ adders having only addition terminals and to utilize phase inverter circuits or the like instead.

Although no practical circuits are illustrated in regard to the above embodiments, they can be easily realized with known techniques. Therefore, only a phase shifter for use in the present invention will be briefly explained with reference to FIGS. 5 and 6. In FIG. 5, R R designate resistance elements, C C capacitance elements, and T and T transistors. A predetermined phase shift can be performed by approfrequency characteristics in thecase where the phase was intended to shift by .withphase shifters having the construction of FIG. 5 and differing in the amount of phase shift. It is shown that the phase was shifted by substantially 90 over Hz l0 k-Hz of the sound signal. 1

While, for brevity of the explanation, the case of the 4-channel sound signals for which the present invention has the greatest possibility of practical use has been described thus far, the invention is further applicable to the cases of 6 channels, 8 channels, 9 channels, 16 channels and 24 channels. For example, in the ease of 8 channels, and equation for reproducing original sig- 15 nals becomes as below in correspondence with Eq. 2.

In this case, however, unlike those in Eq. 2, 7 denotes a phase shift of 45 and accordingly 1' 45 in Eq. 5.

When the matrix of Eq. 5 is factorized, the following equation 6 is obtained.

To be added is that, for the signal generating circuit or coding circuit, the quantities P P T T and 7 in the above equation may be substituted by T T S priately setting the values of the elements. FIG. 6 shows 40 S and 7", respectively.

P 0 PL} 1 1 o o o o o o l o 1 '6 0 o o o o o o 1 '5 o 0 o o o o o 1 1 o o 0 o o o o 1 z o o o o o o o 1 Z' 0 o o o o o o 1 t' o 1 o o o 0 0 l 1 o 1 o 0 o o o o o 1 0 (f o o o o '0 1 1 0 o 1 o o o 0 o 1 o 1 o 'o 0 o 0 o 0 1 o o 0 o 0 o 1 o 4' Since T's representative of the phase shifts are contained by only ten in the above equation 6, l0,phase shifter circuits suffice. Moreover, it is possible to commonly use the phase shifter circuits, with the result that five phase shifter circuits suffice. With the original form of Eq. 5, even if simplifications are made using the relations of 7 1, 7' l etc., approximately 16 rs will still remain. This means the necessity for a number of phase shifter circuits, and becomes a disadvantage in bringing the matrices into the actual circuit.

As apparent from the above description, in accordance with the present invention, with the merits of the universal matrix system kept, it-is possible to simplify the reproduction system and to decrease the number of the expensive phase shifter circuits. The reproducing system for use in the universal matrix system will come into wide use as the so-called 4-channel stereo even in thegeneral homes, and the effect of simplifying the system according to the present invention is great.

What is claimed is:

l. A matrix circuitcomprising first, second, third, and fourth input terminals; first arithmetic circuit means for'adding signals provided from said first and second input terminals; second arithmetic circuit means for subtracting said signal of said second input terminal from said signal of said first input terminal; third arithmetic circuit means for adding signals from said third and fourth input terminals; fourth arithmetic circuit means for subtracting said signal of said fourth input terminal from said signal of said third input terminal; first, second, and third phase shifters having a first phase shift which are respectively connected to the outputs of said first, second, and third arithmetic circuit means; a fourth phase shifter having a second phase shift connected to the output of said fourth arithmetic circuit means, fifth arithmetic circuit means for adding the outputs of said first and third phase shifters; sixth arithmetic circuit means for subtracting the output of said fourth phase shifter from the output of said second phase shifter; seventh arithmetic circuit means for subtracting said output of said third phase shifter from said output of said first phase shifter; eighth arithmetic circuit means for subtracting said output of said second phase shifter from said output of said fourth phase shifter; and first, second, third, and fourth output terminals which are respectively connected to said fifth, sixth, seventh, and eighth arithmetic circuit means; the phase difference between said first and second phase shifts being 90.

I 1" o o 0 T t 1 o ,0 T

0 o 0 TL.

-1 o o T,

0 o 1 J T7 2. A matrix circuit comprising first, second, third, and fourth input terminals; first, second, third, and fourth phase shifters having a first phase shift which are respectively connected to said first, second, third, and fourth input terminals; first arithmetic circuit means for subtracting a signal of said fourth input terminal from a signal of said third input terminal; a fifth phase shifter having a second phase shift connected to the output of said first arithmetic circuit means; second arithmetic circuit means for producing a sum among outputs of said first, second, third, and fourth phase shifters; third arithmetic circuit means for subtracting said output of said second phase shifter from a sum between said outputof said first phase shifter and an output of said fifth phase shifter; fourth arithmetic circuit means for subtracting said outputs of said third and fourth phase shifters from a sum between said outputs of said first and second phase shifters; and fifth arithmetic circuit means for subtracting said output of said second phase shifter and said output of said fifth phase shifter from said output of said first phase shifter; the the phase difference between said first and second phase shifts being and first, second, third, and fourth output terminals respectively connected to said second, third fourth, and fifth arithmetic circuit means.

3. Multi-channel sound system having first matriicircuit for encoding four directional input signals obtained from four signal sources arranged in such man ner that their azimuths on a plane are spaced by approximately 90, a plurality of transmission channel: for transmitting or recording the output signals of the first matrix circuit and a second matrix circuit for decoding the transmitted signal and reproducing fout directional output sound signals correlated with the input signals, wherein said matrix circuits include first second, third, and fourth input terminals; first arithme tic circuit means for adding the outputs of said first ant second input terminals; second arithmetic circui means for subtracting said signal of said second inpu terminal from said signal of said first input terminal third arithmetic circuit means for adding signals fron said third and fourth input terminals; fourth arithmetit circuit means for subtracting said signal of said fourtl input terminal from said signal of said third input termi nal; first, second, and third phase shifters having a firs phase shift which are respectively connected to th outputs of said first, second, and third arithmetic cir cuit means; a fourth phase shifter having a secont phase shift connected to the output of said fourth arithmetic circuit means, fifth arithmetic circuit means for adding the outputs of said first and third phase shifters; sixth arithmetic circuit means for subtracting the output of said fourth phase shifter from the output of said second phase shifter; seventh arithmetic circuit means for subtracting said output of said third phase shifter from said output of said first phase shifter; eighth arithmetic circuit means for subtracting said output of said second phase shifter from said output of said fourth phase shifter; and first, second, third, and fourth output terminals which are respectively connected to said fifth, sixth, seventh, and eighth arithmetic circuit means; the phase difference between said first and second phase shifts being 90.

4. Multi-channel sound system according to claim 3, wherein the transmission channel consists of two transmission channels, one of which connects the first output terminal of the first matrix circuit to the first input terminal of the second matrix circuit and another one of which connects the third output terminal of said first matrix circuit to the third input terminal of said second matrix circuit.

5. Multi-channel sound system according to claim 3, wherein the transmission channels are made up of four transmission channels which transmit the outputs of the first, second, third, and fourth output terminals of the first matrix circuit to first, second, third, and fourth input terminals of the second matrix circuit, respectively.

6. Multi-channel sound system having a first matrix circuit for encoding a four directional input signal obtained from four signal sources arranged in such manner that their azimuths on a plane are spaced by approximately 90, a plurality of transmission channels for transmitting the output signals of the signals of the first matrix circuit and a second matrix circuit for decoding the transmitted signal and reproducing directional output sound signals correlated with the input signals, wherein said matrix circuit includes first, sec- 0nd, third, and fourth input terminals; first, second, third, and fourth phase shifters having a first phase shift which are respectively connected to said first, second, third, and fourth input terminals; first arithmetic circuit means for subtracting a signal of said fourth input terminal from a signal of said third input terminal; a fifth phase shifter having a phase shift connected to the output of said first arithmetic circuit means; second arithmetic circuit means for producing a sum among outputs of said first, second, third, and fourth phase shifters; third arithmetic circuit means for subtracting said output of said second phase shifter from a sum between said output of said first phase shifter and an output of said fifth phase shifter; fourth arithmetic circuit means for subtracting said outputs of said third and fourth phase shifters from a sum between said outputs of said first and second phase shifters; and fifth arithmetic circuit means for subtracting said output of said second phase shifter and said output of said fifth phase shifter from said output of said first phase shifter; the phase difference between said first and second phase shifts being ;and first, second, third, and fourth output terminals respectively connected to said second, third, fourth, and fifth arithmetic circuit means.

7. Multi-channel sound system according to claim 6, wherein the transmission channel consists of two transmission channels, one of which connects the first output terminal of the first matrix circuit to the first input terminal of the second matrix circuit, and the other one of which channels connects the third output terminal of said first matrix circuit to the third input terminal of said second matrix circuit.

8. Multi-channel sound system according to claim 6, wherein the transmission channels are made up of four transmission channels which transmit the outputs of the first, second, third, and fourth output terminals of the first matrix circuit to the first, second, third, and fourth input terminals of said second matrix circuit, respectively. 

1. A matrix circuit comprising first, second, third, and fourth input terminals; first arithmetic circuit means for adding signals provided from said first and second input terminals; second arithmetic circuit means for subtracting said signal of said second input terminal from said signal of said first input terminal; third arithmetic circuit means for adding signals from said third and fourth input terminals; fourth arithmetic circuit means for subtracting said signal of said fourth input terminal from said signal of said third input terminal; first, second, and third phase shifters having a first phase shift which are respectively connected to the outputs of said first, second, and third arithmetic circuit means; a fourth phase shifter having a second phase shift connected to the output of said fourth arithmetic circuit means, fifth arithmetic circuit means for adding the outputs of said first and third phase shifters; sixth arithmetic circuit means for subtracting the output of said fourth phase shifter from the output of said second phase shifter; seventh arithmetic circuit means for subtracting said output of said third phase shifter from said output of said first phase shifter; eighth arithmetic circuit means for subtracting said output of said second phase shifter from said output of said fourth phase shifter; and first, second, third, and fourth output terminals which are respectively connected to said fifth, sixth, seventh, and eighth arithmetic circuit means; the phase difference between said first and second phase shifts being 90*.
 2. A matrix circuit comprising first, second, third, and fourth input terminals; first, second, third, and fourth phase shifters having a first phase shift which are respectively connected to said first, second, third, and fourth input terminals; first arithmetic circuit means for subtracting a signal of said fourth input terminal from a signal of said third input terminal; a fifth phase shifter having a second phase shift connected to the output of said first arithmetic circuit means; second arithmetic circuit means for producing a sum among outputs of said first, second, third, and fourth phase shifters; third arithmetic circuit means for subtracting said output of said second phase shifter from a sum between said output of said first phase shifter and an output of said fifth phase shifter; fourth arithmetic circuit means for subtracting said outputs of said third and fourth phase shifters from a sum between said outputs of said first and second phase shifters; and fifth arithmetic circuit means for subtracting said output of said second phase shifter and said output of said fifth phase shifter from said output of said first phase shifter; the the phase difference between said first and second phase shifts being 90*; and first, second, third, and fourth output terminals respectively connected to said second, third, fourth, and fifth arithmetic circuit means.
 3. Multi-channel sound system having first matrix circuit for encoding four directional input signals obtained from four signal sources arranged in such manner that their azimuths on a plane are spaced by approximately 90*, a plurality of transmission channels for transmitting or recording the output signals of the first matrix circuit and a second matrix circuit for decoding the transmitted signal and reproducing four directional output sound signals correlated with the input signals, wherein said matrix circuits include first, second, third, and fourth input terminals; first arithmetic circuit means for adding the outputs of said first and second input terminals; second arithmetic circuit means for subtracting said signal of said second input terminal from said signal of said first input terminal; third arithmetic circuit means for adding signals from said third and fourth input terminals; fourth arithmetic circuit means for subtracting said signal of said fourth input terminal from said signal of said third input terminal; first, second, and third phase shifters having a first phase shift which are respectively connected to the outputs of said first, second, and third arithmetic circuit means; a fourth phase shifter having a second phase shift connected to the output of said fourth arithmetic circuit means, fifth arithmetic circuit means for adding the outputs of said first and third phase shifters; sixth arithmetic circuit means for subtracting the output of said fourth phase shifter from the output of said second phase shifter; seventh arithmetic circuit means for subtracting said output of said third phase shifter from said output of said first phase shifter; eighth arithmetic circuit means for subtracting said output of said second phase shifter from said output of said fourth phase shifter; and first, second, third, and fourth output terminals which are respectively connected to said fifth, sixth, seventh, and eighth arithmetic circuit means; the phase difference between said first and second phase shifts being 90*.
 4. Multi-channel sound system according to claim 3, wherein the transmission channel consists of two transmission channels, one of which connects the first output terminal of the first matrix circuit to the first input terminal of the second matrix circuit and another one of which connects the third output terminal of said first matrix circuit to the third input terminal of said second matrix circuit.
 5. Multi-channel sound system according to claim 3, wherein the transmission channels are made up of four transmission channels which transmit the outputs of the first, second, third, and fourth output terminals of the first matrix circuit to first, second, third, and fourth input terminals of the second matrix circuit, respectively.
 6. Multi-channel sound system having a first matrix circuit for encoding a four directional input signal obtained from four signal sources arranged in such manner that their azimuths on a plane are spaced by approximately 90*, a plurality of transmission channels for transmitting the output signals of the signals of the first matrix circuit and a second matrix circuit for decoding the transmitted signal and reproducing directional output sound signals correlated with the input signals, wherein said matrix circuit includes first, second, third, and fourth input terminals; first, second, third, and fourth phase shifters having a first phase shift which are respectively connected to said first, second, third, and fourth input terminals; first arithmetic circuit means for subtracting a signal of said fourth input terminal from a signal of said third input terminal; a fifth phase shifter having a phase shift connected to the output of said first arithmetic circuit means; second arithmetic circuit means for producing a sum among outputs of said first, second, third, and fourth phase shifters; third arithmetic circuit means for subtracting said output of said second phase shifter from a sum between said output of said first phase shifter and an output of said fifth phase shifter; fourth arithmetic circuit means for subtracting said outputs of said third and fourth phase shifters from a sum between said outputs of said first and second phase shifters; and fifth arithmetic circuit means for subtracting said output of said second phase shifter and said output of said fifth phase shifter from said output of said first phase shifter; the phase difference between said first and second phase shifts being 90*;and first, second, third, and fourth output terminals respectively connected to said second, third, fourth, and fifth arithmetic circuit means.
 7. Multi-channel sound system according to claim 6, wherein the transmission channel consists of two transmission channels, one of which connects the first output terminal of the first matrix circuit to the first input terminal of the second matrix circuit, and the other one of which channels connects the third output terminal of said first matrix circuit to the third input terminal of said second matrix circuit.
 8. Multi-channel sound system according to claim 6, wherein the transmission channels are made up of four transmission channels which transmit the outputs of the first, second, third, and fourth output terminals of the first matrix circuit to the first, second, third, and fourth input terminals of said second matrix circuit, respectively. 